1. Field of the Invention
The present invention relates to a fuzzy system, and in particular, to a membership function unit to be employed for a fuzzy inference, to a fuzzy inference apparatus executing an inference in conformity with a predetermined fuzzy processing rule, and to a support apparatus to be used in a construction of a fuzzy control system for facilitating development of the system.
2. Description of the Related Art
In accordance with the fuzzy theory, it is possible to represent senses of human beings by utilizing membership functions as means to numerically express such senses.
The human senses characteristically change depending on situations and environments of a human being. For example, let us consider a temperature of water in a Japanese bath. Since the senses vary between the seasons of the year, the judgement of an appropriate temperature suitable for the bath changes depending on each season. In general, when the outdoor or environmental temperature is higher, a slightly warmer temperature of the water is likely to be desired. Namely, the suitable temperature is assumed such that a slightly lower temperature and a slightly higher temperature are appropriate in summer and winter, respectively.
As describe above, owing to the difference in the senses with respect to the temperature of water, as shown in the graphs of FIGS. 26a to 26c, membership functions representing the appropriate temperatures of water develop different contours in association with environmental temperatures.
The graph of FIG. 26a shows a membership function developed when the environmental temperature is 20.degree. C. in which when the temperature rises to 30.degree. C., the graph shifts toward the direction of the lower temperature as shown in FIG. 26b, whereas when the temperature lowers to 10.degree. C., the graph is displaced toward the direction of the higher temperature as shown in FIG. 26c.
The membership functions .mu..sup.20.sub.A (t), .mu..sup.20.sub.B (t), and .mu..sup.20.sub.C (t) representing the senses of "lukewarm", "appropriate temperature", and "hot" at the environmental temperature 20.degree. C. are expressed as follows. EQU .mu..sup.20.sub.A (t)=[1.LAMBDA.-1/2(t-42)]V 0 (1) EQU .mu..sup.20.sub.B (t)=[1/2(t-40).LAMBDA.-1/2(t-44)]V 0 (2) EQU .mu..sup.20.sub.C (t)=[1/2(t-42).LAMBDA.1]V 0 (3)
In these expressions (1) to (3), .LAMBDA. and V denote MIN and MAX operations, respectively.
Similarly, the membership functions at the environmental temperatures 30.degree. C. and 10.degree. C. are respectively represented by the following expressions (4) to (6) and (7) to (9). EQU .mu..sup.30.sub.A (t)=[1.LAMBDA.-1/2(t-40)]V 0 (4) EQU .mu..sup.30.sub.B (t)=[1/2(t-38).LAMBDA.-1/2(t-42)]V 0 (5) EQU .mu..sup.30.sub.C (t)=[1/2(t-40).LAMBDA.1]V 0 (6) EQU .mu..sup.10.sub.A (t)=[1.LAMBDA.-1/2(t-44)]V 0 (7) EQU .mu..sup.10.sub.B (t)=[1/2(t-42).LAMBDA.-1/2(t-46)]V 0 (8) EQU .mu..sup.10.sub.C (t)=[1/2(t-44).LAMBDA.1]V 0 (9)
In the conventional fuzzy system, a plurality of membership functions are required to be defined for the respective environmental temperatures in advance. If it is desired to establish correspondences with respect to all possible environmental temperatures, an infinite number of membership functions are required to be defined.
In order to cope with the variation in the sense above, there has been proposed a method in which the environmental temperature is assumed to be an element or a factor (an external disturbance) increasing ambiguity of the sense so as to adopt a membership function (as shown in FIG. 27) obtained through a composition utilizing a plurality of membership functions.
The graph of FIG. 27 shows membership functions developed when the environmental temperature deviates in a range from 10.degree. C. to 30.degree. C. centered on 20.degree. C. The membership function representing the appropriate temperature extends in the water temperature range from 38.degree. C. to 46.degree. C. When the width of the range is narrower, the ambiguity of the membership function expressing the suitable temperature is decreased. However, in the method associated with this graph, and membership function possesses an enlarged width, namely, an increased ambiguity, which leads to a problem that an appropriate inference cannot be easily accomplished.
Incidentally, in general, according to fuzzy control, when an input signal is supplied, for example, form a sensor to a fuzzy inference apparatus, a group of fuzzy inference rules are used to achieve an inference operation such that based on a result of the inference operation of each inference rule, the apparatus decides a control operation of a control object. The fuzzy inference apparatus includes a fuzzy inference antecedent processing section and a fuzzy inference consequent processing section, so that the inference outputs of the respective inference rules are fed from the component section to a concluding or composing section, which achieves a composition by use of the inference outputs. For example, the output of a definite or determinant value is generated so as to be delivered to the control object.
In the control system of this kind, there may occur a case where an abnormality signal is received from a sensor or the like or where a decrease in a signal level lowers the reliability of the input signal from the sensor. In such a situation, it is not appropriate to directly supply the control object with the determinant value output as the final output from the fuzzy inference apparatus. Consequenty, as shown in FIG. 28, a final decision section 92 is disposed on the output side of a fuzzy inference apparatus 91 so as to determine presence or absence of an exception signal such as an abnormality signal such that depending on the result of determination, the determinant output from the fuzzy inference apparatus 91 is delivered as the final output or an abnormality output is produced.
However, in such a method, there is required the final decision section 92, which necessitates excessive circuit configurations and devices and hence soars the cost of the apparatus.
In order to cope with the problem above, there has been employed a fuzzy inference apparatus 93 (shown in FIG. 29) in which the inference rules include propositions or statements related to exception signals. In this method, however, the exception signals are required to be incorporated as propositions of the inference rules, which leads to a problem that the inference rules become complicated.
Furthermore, certainty of each inference rule can be determined by use of the membership function in the fuzzy inference antecedent and consequent processing sections. However, in a case where such certainty is desired to be altered, it is necessary to set a membership function for each inference rule, namely, the corresponding operation is troublesome.
When a fuzzy control system is to be configured for a control system, it is necessary to produce an application system including fuzzy inference rules and membership functions most suitable for the control system. In a case of development of an application system to conduct the fuzzy control by use of a microprocessor and storage, data items of fuzzy inference rules and membership functions as well as fuzzy inference programs have been conventionally developed for each application.
However, because of necessities of development of the data items of fuzzy inference rules and membership functions and fuzzy inference programs for each application, the development efficiency is considerably lowered. Moreover, an evaluation of the fuzzy inference rules and the membership functions of the application thus developed cannot be accomplished without connecting the system to the actual control system. In consequence, the system development requires a very long period of time.